BizSim

The World of Business—in a Box

John L. Casti

The Computer as a Laboratory

The central process distinguishing science from its competitors—religion, music, litera-

ture, mysticism—in the reality-generation business is the so-called scientific method. An

integral part of this method by which we arrive at scientific “truth,” is the ability to do

controlled, repeatable laboratory experiments by which hypotheses about the phenomenon

under investigation can be tested. It is just such experiments that on a good day lead to

the theories and paradigms constituting today’s “scientific” world view. And, more than

anything else, it is the inability to perform experiments of this type that separate the

natural sciences from the worlds of social and behavioral phenomena. In the latter, we

have no way of doing the experiments necessary to create a bona fide scientific theory of

processes like stock market dynamics, road-traffic flow, and organizational restructuring.

In an earlier, less discerning era, it was often claimed that the realm of human social

behavior was beyond the bounds of scientific analysis, simply because human beings are

“complex”, “unpredictable”, “display free will”, “act randomly”, and so on and so forth.

It’s hard to believe that any modern system theorist would do anything but laugh at such

childish and naıve attitudes to the creation of workable and worthwhile scientific theories

of social and behavioral phenomena. The major barrier to bringing the social beneath

the umbrella of science is not the non-explanations just given in quotes, but the fact that

until now we have had no way to test hypotheses and, therefore, make use of the scientific

method in the creation of theories of social behavior. Now we do. And that laboratory in

which we do our experiments is the digital computer. Let me illustrate with an example

from the world of finance.

Booms and Busts, Bubbles and Crashes

In the fall of 1987, W. Brian Arthur, an economist from Stanford, and John Holland, a

computer scientist from the University of Michigan, were sharing a house in Santa Fe while

both were visiting the Santa Fe Institute. During endless hours of evening conversations

over numerous beers, Arthur and Holland hit upon the idea of creating an artificial stock

market inside a computer, one that could be used to answer a number of questions that

people in finance had wondered and worried about for decades. Among those questions

were:

• Does the average price of a stock settle down to its so-called fundamental value—the

value determined by the discounted stream of dividends that one can expect to receive

by holding the stock indefinitely?

• Is it possible to concoct technical trading schemes that systematically turn a profit

greater than a simple buy-and-hold strategy?

• Does the market eventually settle into a fixed pattern of buying and selling? In other

words, does it reach “stationarity”?

• Alternately, does a rich “ecology” of trading rules and price movements emerge in the

market?

Arthur and Holland knew that the conventional wisdom of finance argued that today’s

price of a stock is simply the discounted expectation of tomorrow’s price plus the dividend,

given the information available about the stock today. This theoretical price-setting proce-

dure is based on the assumption that there is an objective way to use today’s information

to form this expectation. But the information available typically consists of past prices,

trading volumes, economic indicators, and the like. So there may be many perfectly defen-

sible ways based on many different assumptions to statistically process this information in

order to forecast tomorrow’s price. For example, we could say that tomorrow’s price will

equal today’s price. Or we might predict that the new price will be today’s price divided

by the dividend rate. And so on and so forth.

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The simple observation that there is no single, best way to process information led

Arthur and Holland to the not-very-surprising conclusion that deductive methods for fore-

casting prices are, at best, an academic fiction. As soon as you admit the possibility

that not all traders in the market arrive at their forecasts in the same way, the deductive

approach of classical finance theory, which relies upon following a fixed set of rules to

determine tomorrow’s price, begins to break down. So a trader must make assumptions

about how other investors form expectations and how they behave. He or she must try to

psyche out the market. But this leads to a world of subjective beliefs and to beliefs about

those beliefs. In short, it leads to a world of induction in which we generalize rules from

specific observations rather than one of deduction.

In order to address these kinds of questions, Arthur, Holland and their colleagues

constructed an electronic stock market, in which they could manipulating trader’s strate-

gies, market parameters, and all the other things that cannot be done with real exchanges.

The traders in this market are assumed to each summarize recent market activity by a

collection of descriptors, which involve verbal characterization like “the price has gone up

every day for the past week,” or “the price is higher than the fundamental value,” or “the

trading volume is high.” Let us label these descriptors A, B, C, and so on. In terms of the

descriptors, the traders decide whether to buy or sell by rules of the form: “If the market

fulfills conditions A, B, and C, then buy, but if conditions D, G, S, and K are fulfilled,

then hold.” Each trader has a collection of such rules, and acts in accordance with only

one rule at any given time period. This rule is the one that the trader views as his or her

currently most accurate rule.

As buying and selling goes on in the market, the traders can reevaluate their different

rules by assigning higher probability of triggering a given rule that has proved profitable

in the past, and/or by recombining successful rules to form new ones that can then be

tested in the market. This latter process is carried out by use of what is called a genetic

algorithm, which mimics the way nature combines the genetic pattern of males and females

of a species to form a new genome that is a combination of those from the two parents.

A run of such a simulation involves initially assigning sets of predictors to the traders

at random, and then beginning the simulation with a particular history of stock prices,

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interest rates, and dividends. The traders then randomly choose one of their rules and

use it to start the buying-and-selling process. As a result of what happens on the first

round of trading, the traders modify their estimate of the goodness of their collection of

rules, generate new rules (possibly), and then choose the best rule for the next round of

trading. And so the process goes, period after period, buying, selling, placing money in

bonds, modifying and generating rules, estimating how good the rules are, and, in general,

acting in the same way that traders act in real financial markets.

A typical frozen moment in this artificial market is displayed in Figure 1. Moving

clockwise from the upper left, the first window shows the time history of the stock price

and dividend, where the current price of the stock is the black line and the top of the

grey region is the current fundamental value. The region where the black line is much

greater than the height of the grey region represents a price bubble, whereas the market

has crashed in the region where the black line sinks far below the grey. The upper right

window is the current relative wealth of the various traders, and the lower right window

displays their current level of stock holdings. The lower left window shows the trading

volume, where grey is the number of shares offered for sale and black is the number of

shares that traders have offered to buy. The total number of trades possible is then the

smaller of these two quantities, because for every share purchased there must be one share

available for sale.

After many time periods of trading and modification of the traders’ decision rules,

what emerges is a kind of ecology of predictors, with different traders employing differ-

ent rules to make their decisions. Furthermore, it is observed that the stock price always

settles down to a random fluctuation about its fundamental value. However, within these

fluctuations a very rich behavior is seen: price bubbles and crashes, market moods, over-

reactions to price movements, and all the other things associated with speculative markets

in the real world.

The agents in the stockmarket simulation are individual traders. A quite different type

of business simulation emerges when we want to look at an entire industry, in which case

the agents become the individual firms constituting that industry. The world’s catastrophe

insurance industry served as the focus for just such a simulation exercise called Insurance

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Figure 1. A frozen moment in the surrogate stock market.

World, carried out by the author and colleagues at the Santa Fe Institute and Intelligize,

Inc. over the past couple of years.

Insurance World

As a crude, first-cut, the insurance industry can be regarded as an interplay among three

components: firms, which offer insurance, clients, who buy it, and events, which determine

the outcomes of the “bets” that have been placed between the insurers and their clients.

In Insurance World, the agents consist of primary casualty insurers and the reinsurers,

the firms that insure the insurers, so to speak. The events are natural hazards, such as

hurricanes and earthquakes, as well as various external factors like government regulators

and the global capital markets.

Insurance World is a laboratory for studying questions of the following sort:

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• Optimal Uncertainty: While insurers and reinsurers talk about getting a better

handle on uncertainty so as to more accurately assess their risk and more profitably price

their product, it’s self-evident that perfect foreknowledge of natural hazards would spell

the end of the insurance industry. On the other hand, complete ignorance of hazards is

also pretty bad news, since it means there is no way to weight the bets the firms make

and price their product. This simple observation suggests that there is some optimal level

of uncertainty at which the insurance—but perhaps not their clients—can operate in the

most profitable and efficient fashion. What is that level? Does it vary across firms? Does

it vary between reinsurers, primary insurers, and/or end consumers?

• Industry Structure: In terms of the standard metaphors used to characterize organ-

izations—a machine, a brain, an organism, a culture, a political system, a psychic prison—

which type(s) most accurately represents the insurance industry? And how is this picture

of the organization shaped by the specific “routines” used by the decisionmakers in the

various components making up the organization?

The simulator calls for the management of each firm to set a variety of parameters

having to do with their desired market share in certain regions for different types of hazards

and level of risk they want to take on, as well as to provide a picture of the external

economic climate (interest rates, likelihood of hurricanes/earthquakes, inflation rates and

so forth). The simulation then runs for 10 years in steps of one quarter, at which time

a variety of outputs can be examined. For instance, Figure 2 shows the market share for

Gulf Coast hurricane insurance of the five primary insurers in this toy world, under the

assumption that the initial market shares were almost identical—but not quite. In this

experiment, firm 2 has a little larger initial market share than any of the other firms, a

differential advantange that it then uses to squeeze out all the other firms at the end of

the ten-year period. This is due to the “brand effect,” in which buyers tend to purchase

insurance from companies that they know about.

As a final example of what simulation and business have to say to each other, con-

sider the movement of shoppers in a typical supermarket. This world is dubbed SimStore

by Ugur Bilge of SimWorld, Ltd. and Mark Venables at J. Sainsbury in London, who

collaborated with the author on its creation.

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Figure 2. Market share distribution for five primary insurers.

SimStore

The starting point for SimStore is a real supermarket in the Sainsbury chain, one located

in the London region of South Ruislip. The agents are individual shoppers who frequent

this store. These electronic shoppers are dropped into the store, and then make their way

to the various locations in the store by rules such as “wherever you are now, go to the

location of the nearest item on your shopping list,” so as to gather all the items they want

to purchase.

As an example of one of the types of outputs generated by SimStore, customer checkout

data are used to calculate customer densities at each location. Color codes are with

descending order: blue, red, purple, orange, pink, green, cyan, grey and nothing. Using

the Manhattan metric pattern of movement, in which a customer can only move along the

aisles of the store, all locations above 30 percent of customer densities have been linked

to form a most popular customer path. Once this path is formed a genetic algorithm will

minimize (or maximize!) the length of the overall shopping path.

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In the same store, this time each individual customer path has been internally cal-

culated using the simple “nearest neighbor” rule noted above. All customer paths have

been summed for each aisle, in order to calculate the customer path densities. These den-

sities are displayed in Figure 3 as a relative density map using the same color code just

mentioned.

Figure 3. Customer densities along each aisle in the simulated store.

Simulation is Good for Business

Large-scale, agent-based simulations of the type discussed here are in their infancy. But

even the preliminary exercises outlined here show the promise of using modern computing

technology to provide the basis for doing experiments that have never been possible before.

Even better, these experiments are exactly the sort called for by the scientific method—

controlled and repeatable—so that for the first time in history we have the opportunity to

actually create a science of human affairs. If I were placing bets on the matter, I’d guess

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that the world of business and commerce will lead the charge into this new science that

will form during the 21st century.

References

Casti, J. Would-Be Worlds. New York: Wiley, 1997.

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